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M and A question - Must Try

by imhimanshu » Tue Sep 13, 2011 5:16 am
A fruit drink advertises that it has 5% apple juice. Children pour themselves ¾ cup of this fruit drink and then add ¼ cup of fruit drink that has 50% apple juice. Which is most nearly the percent of apple juice in the children's mixed drink?
1 - 12.5%
2 - 16.3%
3- 17.5%
4- 55.0%
5- 65.0%

how do you go about it. I am unable to answer this
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by sl750 » Tue Sep 13, 2011 5:29 am
I suppose you have to find the concentration of apple juice in the final mixture

A's concentration is 5%
B's concentration is 50%

3/4*1/20 + 1/4*1/2 = 3/80 + 1/8 = 13/80 = 16.25%
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by knight247 » Tue Sep 13, 2011 5:36 am
Let the capacity of 1 cup be x litres.

3/4th of the cup has 5% apple juice i.e. 3x/4 contains 5% apple juice. The actual volume of apple juice is given by

(5/100)*(3x/4)=15x/400

Now 1/4th cup consists of 50% apple juice. So 1/4th of x contains 50% apple juice. The actual volume of apple juice is given by
(50/100)*(x/4)=50x/400

Now the important thing to remember is that the actual apple juice content in the final mixture equals the sum of the apple juice contents in each of the two components. So volume of apple juice in the final mixture=15x/400+50x/400=65x/400=13x/80

(13/80)*100=16.25% Hence B
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by imhimanshu » Tue Sep 13, 2011 6:42 am
Thanks Knight. I can see my mistake now.
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by rohit_gmat » Tue Sep 13, 2011 9:22 am
imhimanshu wrote:A fruit drink advertises that it has 5% apple juice. Children pour themselves ¾ cup of this fruit drink and then add ¼ cup of fruit drink that has 50% apple juice. Which is most nearly the percent of apple juice in the children's mixed drink?
1 - 12.5%
2 - 16.3%
3- 17.5%
4- 55.0%
5- 65.0%

how do you go about it. I am unable to answer this
i wud recommend plugging in.. either 100 or 400 wud be a good number.. will take 100 to keep fewer steps but we will have to work with fractions..

so we have 100ml of juice 1, which has 5ml of apple juice in it... kids pour 75 ml of tht juice in a cup (which brings 15/4 ml of apple juice into our cup)..
then we have 100 ml of juice 2, which as 50ml of apple juice in it... kids pour 25 ml of tht juice into their cup (which brings 50/4 ml of apple juice into our cup)..
so the total amount of apple juice tht we get into our 100 ml mixed cup is... (15/4) + (50/4) = 65/4 = approx 16 ml which will be 16% ...
AC B
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by GMATGuruNY » Tue Sep 13, 2011 10:08 am
imhimanshu wrote:A fruit drink advertises that it has 5% apple juice. Children pour themselves ¾ cup of this fruit drink and then add ¼ cup of fruit drink that has 50% apple juice. Which is most nearly the percent of apple juice in the children's mixed drink?
1 - 12.5%
2 - 16.3%
3- 17.5%
4- 55.0%
5- 65.0%

how do you go about it. I am unable to answer this
This is a weighted average question.
Out of every 4 liters, 3 liters will be 5% apple juice and 1 liter will be 50% apple juice.
We want the percentage of apple juice in the mixture.

This problem is no different from the following:
3 melons weigh 5 pounds each and 1 melon weighs 50 pounds.
What is the average weight of all 4 melons?

(3*5 + 1*50)/4 = 65/4 ≈ 16.

The correct answer is B
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by studentps2011 » Fri Sep 16, 2011 12:14 pm
An equation for solving such types of mixture problems:

w1/w2 = (A2 - Aavg)/(Aavg - A1)

So, the solution to the problem becomes
(3/4)/(1/4) = (50-x) / (x-5)

Solving for x; x=16.3
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